28-05-2025

2001CJA101021250009 JA

PHYSICS

SECTION-I(i)

1) A ring of radius R is placed in the plane with its centre at origin and its axis along the x-axis and
having uniformly distributed positive charge. A ring of radius r(<<R) and coaxial with the larger
ring is moving along the axis with constant velocity then the variation of electrical flux (ϕ) passing

through the smaller ring with Position will be best represented by :

(A)

(B)

(C)

(D)

2) q1, q2, q3 and q4 are point charges located at point as shown in the figure and S is a spherical

Gaussian surface of radius R. Which of the following in true according to the Gauss’s law : [ is
electric field due to q1 and so on]

(A)

(B)

(C)

(D) None of these

3) Consider a uniform volume charge distribution

= ρ for 0 ≤ r ≤ R
= –ρ for R < r ≤ 2R
as shown in the figure where r is the radial distance taken from central point of sphere. The electric

field intensity at point P is :

(A)
away from centre

(B)
towards the centre

(C)
away from centre

(D)
towards the centre

4) In the below figure a dielectric is released inside the capacitor at t = 0 from the end of the
capacitor. Then which of the following current (i) Vs time(t) graph is correct in one complete
oscillation. If clockwise current is taken as positive and anticlockwise as negative. (a > c). Neglect

electrical and mechanical resistance.

(A)

(B)

(C)

(D)

SECTION-I(ii)

1) Figure shows two identical capacitors A & B with identical dielectric inserted between them and
are connected to a battery. Now the slab of capacitor B is pulled out with battery connected:

(A) During the process current flows counter clockwise in the circuit.
(B) Finally charge on capacitor B will be less than that on capacitor A.
(C) Electric field in capacitor A reduces in magnitude.
(D) During the process, internal energy of the battery increases.

2) Consider a infinitely long charged cylindrical insulator of uniform volume charge density r as
shown in the figure. There is also a long cylindrical cavity of radius r having its axis parallel to axis
of cylindrical charged body.

(A)
The magnitude of electric field intensity at the xx' axis of charged body is
(B) The magnitude of electric field intensity at axis xx' of charged body is zero

(C)
The magnitude of electric field intensity at axis yy' of charged body is

(D)
The magnitude of electric field intensity at any point in the caivity is .

3) In the figure shown spheres S1, S2 and S3 have radii R, R/2, R/4 respectively. C1, C2 and C3 are
their centres lying in the same plane angle C1C2C3 is right angle. Sphere S3 has a uniformly spread
volume charge density 4ρ. The other spheres S1 and S2 have uniform volume charge density ρ and 2ρ

respectively. Then

(A)
The electric field at a point A at a distance R/8 from C3 on the line C2C3 is

(B)
The electric field at point B at a distance R/4 from C2 on the line C2C3 is

(C)
The electric field at a point A at a distacne R/8 from C3 on the line C2C3 is
(D)
The electric field at point B at a distance R/4 from C2 on the line C2C3 is

SECTION-II(i)

Common Content for Question No. 1 to 2

In the figure, nine capacitors are connected as shown.

1) If a 10V battery is connected across the terminals A & D, then charge drawn from battery is (in
µC) :-

2) If a 10V battery is connected across the terminal B & C then charge in capacitor connected
between A & D is P(µC) & potential difference between terminals E & F is R (volt), then R – P is :

Common Content for Question No. 3 to 4

Given a square frame of diagonal length 2r made of insulating wires. There is a short dipole, having
dipole moment P, fixed in the plane of the figure lying at the center of the square, making an
angle as shown in figure. Four identical particles having charges of magnitude q each and
alternatively positive and negative sign are placed at the four corners of the square. Select the

correct alternative(s).

3) Electrostatic force on the system of four charges due to dipole is Then the value of n
is____.

4) Net torque on the system of four charges about the centre of the square due to dipole is ____.
 SECTION-II(ii)

1) Four identical free charges each of value q are located at the four corners of a square of side a. A

point charge that must be placed at the centre for the system to be in equilibrium is .
Calculate the value of α ? (Consider only electrostatic force)

2) A uniformly charged solid sphere (volume charge density ρ) and infinite line charge (linear charge

density –λ) generates net electric field zero at point P. If , then find the value of x. (P is

in plane of paper)

3) Two oppositely point charged particles of mass 2kg each are kept on a smooth horizontal surface
at distance of 8m. When they starts moving towards each other at time t = 0 due to electrostatic
force, a force of 2N is applied as shown in figure. Find the distance traveled by the positive charge
(in meters) before it collides with negative charge. It is given that the two charges collide at t = 2

seconds.

4) One quadrant is removed from a charged plastic disc with charge density σ. Taking V = 0 at
infinity, determine the potential due to the quadrant at point P, i.e., on the central axis of the
original disc, at a distance y = 3m from the original centre. Radius of disc is 4m. If your answer is

write value of n.

5) Figure shows three concentric conducting shells. Inner and outer shells are connected through
conducting wire. Inner shell is earthed. If outer shell is given a charge Q and potential of middle
shell is found to be N . Find the value of N.

6) Four point charges +Q1, –Q2 , –Q2, and +Q1 are fixed at the
points , and respectively on the y-axis. A particle of mass 6 × 10–4 kg and charge +0.1μC
moves along the x direction. Its speed at x = + ∞ is v0 . Find the least value of v0 for which the
particle will cross the origin. Take |Q1| = 8 |Q2| and |Q2| = 1μC

CHEMISTRY

SECTION-I(i)

1) The decomposition of N2O5 : 2N2O5 → 4NO2 + O2 is studied by measuring the concentration of

oxygen as a function of time, and it is found that

at constant temperature and volume. Under these conditions the reaction goes to completion to the
right. What is the half-life of the reaction under these conditions? (ln2 = 0.693)

(A) 4620 sec.

(B) 2310 sec.
(C) 1155 sec.
(D) None of these

2) Select the incorrect statement about metal carbonyl complex compounds :

(A) Metal carbon bond in metal carbonyls possess both σ and π character
(B) Due to synergic bonding metal carbon bond becomes weak
(C) Due to synergic bonding carbon oxygen bond strength decreases
In metal carbonyls extent of synergic bonding will increase with increase in negative charge on
(D)
central metal ion

3) Identify the compound which contain most acidic hydrogen :

(A)

(B)

(C)

(D)

4) Correct statements for the given reaction are :

A. Compound ‘B’ is aromatic

B. The completion of above reaction is very slow
C. ‘A’ shows tautomerism
D. The bond lengths C-C in compound B are found to be same
Choose the correct answer from the options given below :

(A) A, B and D only

(B) A, B and C only
(C) B, C and D only
(D) A, C and D only

SECTION-I(ii)
1) The order of reaction A → Products, may be given by which of the following expression(s)?

(A)

(B)

(C)

(D)

2) Which of the following compounds are tetrahedral but NOT sp3 hybridised?

(A) K2MnO4
(B) SnI4
(C) CrO2Cl2
2–
(D) [HgI4]

3)
Select the correct statement(s)

(A) A and C are the enol forms of B

(B) A is more stable than C
(C) C is more stable than A
(D) Only A is the enol form of B

SECTION-II(i)

Common Content for Question No. 1 to 2

Ni (NH3)4 (NO3)2. 2H2O molecule may have two or zero unpaired electrons depending on geometrical
arrangement and nature of ligands present inside the coordination sphere.

1) If octahedral complex (from this formula) contains only two oxygen donor ligands inside
coordination sphere and complex does not conduct electricity, what will be the total mass of neutral
ligands present inside coordination sphere (in g) in 1 mole complex? (at wt. of Ni = 58.5)

2) When geometry of complex species is octahedral, what will be the value of its spin only magnetic
moment in BM?

Common Content for Question No. 3 to 4

(1) Geometrical isomerism is possible when compounds have restricted rotation system like
i.e., C = C, C = N, ring, Allene, Spiro etc
(2) Geometrical isomers have different aerial distance between two specified groups. i.e.,

3) Number of compound(s) which cannot show geometrical isomerism?

(1) (2) CH3 – CH = C = CH – CH3 (3)

(4) (5) (6)

(7)

4) How many of the following pair(s) represent geometrical isomers ?

 SECTION-II(ii)

1) Let a weak monobasic acid HA dissociates in aq. solution. Dissociation follows 1st order kinetics.
Initially at 300K acid has C0 concentration and initial rate at 300K is 2 × 10–4 Ms–1

Using above plot what is the pH of the solution after 1st half life. (k =
rate constant of decomposition)

2) How many of the given complexes follow E.A.N. rule ?

(a) [Fe(CO)5] (b) [Co2(CO)8] (c) [Fe(π-C5H5)2]
(d) K3[Fe(CN)6] (e) [Fe(NO)2(CO)2] (f) [CoF6]4–

3) How many of the following anionic ligands act as chelating ligand (bipy) , (ox) , (pn) , (gly) , (acac)
, (trien) , (nta) , (EDTA) , CN–

4)

Consider the following compounds

If P is the number of compounds having more enol content than III, Q is the number of compounds
having enolic form more stable than that of IV and R is the number of compounds having percentage
of enolic form more than the corresponding keto form, find P + Q + R.

5) How many maximum Hydrogen atoms are replaced by D in the following tautomerization.

6) Consider the statements given below:

(a) The possible number of alkynes with the formula C5H8 are ‘X’
(b) The total number of acyclic structural isomers possible for the compound with molecular formula
C4H10O are ‘Y’
(c) Total number of structural isomers possible for the compound with molecular formula C3H6Cl2 are
‘Z’
(d) Total number of 2° amines possible having molecular formula C4H11N are ‘W’
Then find the value of ‘X’ + ‘Y’ + ‘Z’ + ‘W’.

MATHEMATICS

SECTION-I(i)

1) The total number of points of non-differentiability of in is

(A) 40
(B) 30
(C) 20
(D) 10

2) If then

is equal to _________.

(A) 4
(B) 2
(C) 3
(D) 1

3) If L1 = and L2 = , then the value of |L1 – L2|

is equal to

(A) 0

(B)

(C)

(D)

4) If f(x) = sin–1x and g(x) = [sin(cosx)] + [cos(sinx)], (where [.] denotes the greatest integer
function), then range of f(g(x)) is

(A)

(B)

(C)

(D)

SECTION-I(ii)

1) Let and are function defined as ƒ(x) = [x2–4] and g(x) =

|x–2|ƒ(x)+|3x–5| ƒ(x)
(where [y], denotes greatest integer function) Then

(A)
f is discontinuous at exactly 8 points in the interval

(B)
f is discontinuous at exactly 9 points in the interval

(C)
g is non-differentiable at exactly 10 points in the interval

(D)
g is non-differentiable at exactly 9 points in the interval

2) If f(x) = sin–1(x + 2) + cos–1 and g is the inverse of f, then

(A)
(B)

(C)

(D)

3) If exists and is equal to zero then

(A) α + 2β = 6

(B)

(C) 3α + 2β = 0
(D) 3α – 5β = 0

SECTION-II(i)

Common Content for Question No. 1 to 2

ƒ (x) is an odd periodic function with period 6 such that for x ∈ [0, 3),

, (where {.} denotes fractional part function) and ƒ (3) = 0.

On the basis of above information answer the following :

1) Number of points of discontinuity of ƒ (x) in the interval (–9, 9) is -

2) Number of solutions of the equation ƒ (x) = n|x| is -

Common Content for Question No. 3 to 4

Consider,

3) If and range of f(x) is: (a, b) then the value of is

4) The absolute value of is equal to:

SECTION-II(ii)

1)

Number of point(s) in [0, 9], where is discontinuous, is

(where {.} denotes fractional part function)
2) If and then

(B – A) is equal to , where a,b,c,d ∈ N and are in their lowest form, find

3) Let a1, a2, a3, ..... an be a sequence of numbers satisfying

If a1 = 3, then is

4) For a certain value of c, , is finite and non-zero. The value of 3c +

λ is

5) Let f (x) be a differentiable function in [-1, ∞) and f(0) = 1 such that

. Find the value of is

6) Let f(x) = x2 – x + k – 2, k ∈ R. If the complete set of values of k for which y = |ƒ(|x|)| is

non derivable at 5 distinct points is (a, b) then the value of 8(b – a) is
 ANSWER KEYS

PHYSICS

SECTION-I(i)

Q. 1 2 3 4
A. C B B C

SECTION-I(ii)

Q. 5 6 7
A. A,C,D A,C,D A,B

SECTION-II(i)

Q. 8 9 10 11
A. 200.00 4.00 6.00 0.00

SECTION-II(ii)

Q. 12 13 14 15 16 17
A. 2 4 5 4 0 3

CHEMISTRY

SECTION-I(i)

Q. 18 19 20 21
A. B B B D

SECTION-I(ii)

Q. 22 23 24
A. A,C,D A,C A,C

SECTION-II(i)

Q. 25 26 27 28
A. 68.00 2.82 or 2.83 1.00 5.00

SECTION-II(ii)

Q. 29 30 31 32 33 34
A. 2 4 8 9 7 17

MATHEMATICS
 SECTION-I(i)

Q. 35 36 37 38
A. A A C D

SECTION-I(ii)

Q. 39 40 41
A. B,D A,B A,C

SECTION-II(i)

Q. 42 43 44 45
A. 6.00 3.00 0.83 0.33

SECTION-II(ii)

Q. 46 47 48 49 50 51
A. 9 8 1 2 1 2
 SOLUTIONS

PHYSICS

1)
since r << R so we can consider electric field is constant throughtout the surface of smaller
ring, hence

So, the best represented graph is C.

2)
where E → field due to all the charges in space.

3)

= E.F. due to inner charge

= E.F. due to outer charge

6) Apply the concept of Gauss law and principle of super position

for internal point

for external point

7) (A)
(B)

8) Ceq = 4µF + 12µF + 4µF = 20µF

Q = 20µF × 10V = 200 µC

9) Here,
Ceq = 6µF
Q = 60µC

10)
11) Conceptual.

12) (force on charge 4)

For to be zero, each component must be separately zero.

13) ⇒ Enet = 0

⇒x=4

14) Acceleration of system (a) =

displacement of centre of mass of system (x) =

x1 + x2 = 8 &

15)

16) Potential of inner shell is zero, therefore no charge shall reside on any shell.

17)

4x2 + 4a2 = x2 + 9a2

3x2 = 5a2
 = 3 × 9 × 10 + 9 × 1 × 10–6 = 27 × 103v

v = 3 m/s

CHEMISTRY

18)

= 2310 sec.

19)

synergic bonding increases the bond strength of metal and carbon in carbonyls compound and
decreases the bond strength of carbon and oxygen.

21)

Resonance hybrid of B showing all C-C bond length same

22) and

23) K2MnO4 is tetrahedral but its hybridization is d3s, not sp3

Mn (GS) = [Ar]

Mn+6 ion = [Ar]

Mn+6 ion in = [Ar]

[MnO4]2–
CrO2Cl2 is tetrahedral but its hybridization is d3s, not sp3

Cr(GS) = [Ar]

[Hgl4]2– is tetrahedral and its hybridization is sp3.

Hg(GS) = [Kr] 4f14

therefore, the species that are tetrahedral but not sp3 hybridizer are:
K2MnO4 and CrO2Cl2

24) Fact based.

25)

26) Ni+2 (d8) octahedral : 2 unpaired electrons.

29)
log k1 = – 2.3 = –3 + 0.7
K1 = 5 × 10–3

K2 = 10–2
10–2[HA] = 2 × 10–4
⇒ [HA] = 2 × 10–2
After 1st t1/2 [H+] = 10–2M ; pH = –log 10–2 = 2

30) (a, b, c, e)
(d) K3[Fe(CN)6] = 26 - 3 + 2 × 6 = 35 does not follow E.A.N. rule.
(f) [CoF6]4– = 27 - 2 + 2 × 6 = 37 does not follow E.A.N. rule.

31)
 bi-py →

gly → , acac →

EDTA →

out of the given ligand, all act al challenging

except →8

33) Tautomerisable H atom will be replaced by D atom.

34) X = 3, Y = 7, Z = 4, W = 3

MATHEMATICS

35) Here,
Since, and are periodic with period
and in there are 40 points of non-differentiability.

36)
After solving this equation, we get
x = – 1 or x = 0
S = {–1, 0}

=4

39)

f(x) = [x2 - 4],

f(x) = [x2] - 4
continuous at x = 0
Discontinuous at
Total 9 points.
g(x) = |x - 2| f(x) + |3x - 5| f(x)
Here f(x) is not differentiable

Hence N.D at 9 points

40) Domain of f(x) = {–1}

Range of f(x) =
Now, verify alternatives.

41)
for existence of limit α = –3 & β = 9/2

42) In [–3, 3], ƒ (x) is discontinuous at 2 points hence for x ∈ (–9, 9), it will be discontinuous at
2 × 3 = 6 points
Since ƒ (x) is an odd periodic function with period 6, it can be defined for all x ∈ R.
For

43) Graphically number of solutions = 3

44) Putting , we get

45) Putting , we get

47)
Hence a = 5; b = 24; c = 5; d = 6
a + b + c + d = 40

48)

49) We have,

This will be of the form ∞ × 0 only, if

5c – 1 = 0 ⇒ substituting , λ becomes

, where

Hence and ⇒ 3c + λ = 2

50)
51) Both roots of equation x2 – x + k – 2 = 0 must be distinct and positive

then, k ∈
∴ 8 (b – a) = 2